Biostatistics

Phd Kamil Barański

Department of epidemiology

Medical University of Silesia in Katowice

Random variable - a variable whose value changes in an unpredictable, random manner(in the mathematical sense). It can take any value from a certain set of values, and eachof these values can be assigned a certain probability.

Randomness – no visible scheme among e.g. measured variable value.

Population - a set of objects that have at least one thing in common, e.g. a set of "things"that we would like to measure; set of units (objects / measurements) about which we want todraw some conclusions.

Parameter - characteristics of the studied population. Describes what we would liketo estimate. We use Greek letters (µ, σ).

Definitions

Sample - a subset of the population. A set of measurements or observations we have madethat should be representative of our general population.

Random sample - a sample selected e.g. in such a way thateach sample of the same size has the same chance of beingselected.

Statistics - numerical characteristics of the sample we selected.

Definitions

Two meanins of term statistics

✓ section of mathematics

✓ numerical characteristics of the sample

Type of variables

✓ nominal → Is „A” different from „B”?

✓ ordinal → Is „A” greather than „B”?

categorial / qualitative

✓ interval → How many units of „A” are different from „B”?

✓ continuous → How many times „A” is longer than „B”?

Numerical / quantitative

Numeric variables can always be transformed into categorical variables, but not vice versa,

e.g. height [cm] → low, medium, high.

Variables can also be divided by function:

✓ dependent variables

✓ independent variables

Type of variables and their importance due to the possibility of performing mathematical

operations

Different statistical methods depend on the type of variables.

counting ordering + / – * / :

nominal +

categorical + +

interval + + +

zmienne iloczynowe + + + +

Source: lecture prof. J. E. Zejda

Słowniczek, np. LEK2 – antibiotic in the first three days:

0 = no, 1 = vancomycin, 2 = ampicillin, ‘ ‘ = lack of data

Dataset

✓ giving each subject his own unique identification number - no identifying information, e.g. surname,

is entered

✓ simple variable names, e.g. systolic pressure = RR systole

✓ short names, e.g. up to 8 characters in the variable name

✓ avoid unique letters. Exemple: polish letters ć,ą,ż

✓ avoiding units of measurement, e.g. 15%,

Statistica – importing database

Statistica – browsing the database contents

Variable’s name→ „click” mouse button (right) → specification of variable

or

→ double click on variable’s name

Statistica – specification of variable

TEXT LABEL EDITOR → you can enter labels → names for the value of a categorical

variable → attention to the automatic assignment of numerical values.

VALUES, STATISTICS ... → you can quickly check the variable

values before starting the analysis.

ALL SPECIFICATIONS → variable specification editor. You can modify the NAME,

VARIABLE TYPE, NO DATA CODE if you need it.

Statistica – correction of incorrect values

✓ after finding invalid values, delete them

✓ we select the column / variable that we want to correct

✓ card: DATA → RECODE

✓ we replace evidently incorrect values with the missing data

code

✓ if we know the correct value, enter it

Statistica – creating new variable

Variable’s name→ „right click”

Here we can enter the formula we want to calculate.

Statistica – quantitative variable categorization

✓ we create a new variable (new empty column)

✓ select and "click" CODE

✓ we condition new codes, e.g. height categories, with values in another column, e.g.

height values in cm

Measures of central tendency:

✓ average (parametric)

✓ median (non-parametric)

✓ fashion (non-parametric)

✓ quartiles and any centiles (non-parametric)

Measures of variation / dispersion / dispersion:

✓ variance / standard deviation / coefficient of variation (parametric)

✓ range (non-parametric)

✓ range / interquartile range (non-parametric)

Descriptive statistics

Specification:

✓ easy to calculate

✓ uses all information contained in the data

✓ characterizes important distributions → especially Normal distribution for continuous variables N

(µ, σ2)

Limitations:

✓ sensitive to extreme / extreme / outliers

✓ inappropriate as a measure of central tendencies for clearly asymmetrical distributions

✓ limited significance for variables expressed on a categorical scale

Mean value in sample and population

Median

After ordering data from smallest to largest:

✓ for the odd number of observations, the median is the median observation

✓ for an even number of observations, the median is the arithmetic mean of the 2 middle

observations

Specification:

✓ not sensitive to outliers

✓ it is not affected by the shape of the distribution

✓ suitable (also) for the ordinal scale

✓ most frequent value

✓multimodality indicates the heterogeneity of the population

Mode

Range R = Xmax – XminInterquartile range IQR = Q3 – Q1

Q1 → lower quartile

Q2 → middle quartile= median

Q3 → upper quartile

Variance in sample Variance in population

Standard deviation in sample Standard deviation in population

Dispersion

( )22

1

1 N

i

i

xN

=

= −( )22

1

1

1

n

i

i

s x xn =

= −−

Statistica – description of data

STATISTICS → BASIC STATISTICS → DESCRIPTIVE STATISTICS → OK

Variable Selection:

we highlight or enter variable numbers in the edit field

Selecting a set of variables:

continuous list - highlight with Shift pressed or select with the mouse

discontinuous list - we highlight with Ctrl pressed

all variables - the ALL button

EXPAND / COLLECT → long variable names

CLOSE UP → VALUES, STATISTICS window ...

Statistica – Variables

Statistica – karta WIĘCEJ

STATYSTYKA → STATYSTYKI PODSTAWOWE → STATYSTYKI OPISOWE → OK →

karta WIĘCEJ

W tym miejscu możemy obliczyć interesujące nas statystyki opisowe dla zmiennych ilościowych.

Statistica – normal distribution

STATISTICS → BASIC STATISTICS → DESCRIPTIVE STATISTICS → OK →

NORMALITY tab → HISTOGRAMS

Here, we can check the normality of the distribution for the quantitative variable of interest.

p>0,05 = normal distribution

p

✓ for example, when we want to return from a workbook to a window with a data table

✓ when we have more windows, data tables, and workbooks open

Statistica – switching between windows

Statistica – contingency tables

Statistica – estimation of prevelance

References

✓ Zejda J.E., Kowalska M., Brożek G .: "BIOSTATISTICS. Practical methods of data analysis

in observational epidemiological studies". CATFISH

✓ Presentation of prof. dr hab. n. med. Jan E. Zejda. Chair and Department of Epidemiology

WLK ŚUM

✓ Physics presentation Beaty Malec. Chair and Department of Epidemiology WLK ŚUM